The main food-safety issue to be aware of is botulism. Boiling water temperatures do NOT kill botulism spores/bacteria, although it cannot live in high-acid environments. Botulinum toxin is odorless, colorless and tasteless. Thus, you cannot rely on noticing that food is contaminated, and just a small taste can be enough to give you botulism. The disease is often (before modern medicine, usually) fatal. Not to scare you, i'm just saying, Follow Directions Carefully
High-acid foods (tomatoes, certain [but not all] tomato-based sauces, and pickles) can safely be canned in a water-bath canner. You can improvise for small batches with a large stockpot or other kettle type thing.
Low-acid vegetables (corn, beans, anything that isn't a tomato or a pickle) should only be done in a pressure canner.
Fruits can be done in either (it doesn't tend to have botulism problems, but other types of spoilage are still an issue, and pressure-canning reduces the likelihood of that).
Meat/poultry/fish should
definitely only ever be canned in a pressure canner, and with care.
Jams, jellies etc require only a water-bath canner.
You may see older recipes that call for steam-canning or oven-canning, but be aware that these methods are NOT guaranteed to kill all botulism spores and thus are not recommended anymore.
Since a pressure canner is expensive, unless you can borrow one you might want to start out making canned fruit or tomatoes or making pickles, so you can use stuff you already have and see how you like it.
Ball canning co has put out a wonderful book which will tell you all you need to know, it is called something like the Ball Blue Book of Canning. Check your library, and if they don't have it they may be able to get it thru interlibrary loan.
Have fun!
Pat